erweitern (ln(t)+1)^3

Lösung

erweitern

(ln (t) + 1)^{3}

ln^{3} (t) + 3 ln^{2} (t) + 3 ln (t) + 1

Schritte zur Lösung

(ln (t) + 1)^{3}

Wende Formel für perfekte dritte Potenzen an:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

a = ln (t), b = 1

= ln^{3} (t) + 3 ln^{2} (t) \cdot 1 + 3 ln (t) \cdot 1^{2} + 1^{3}

Vereinfache

ln^{3} (t) + 3 ln^{2} (t) \cdot 1 + 3 ln (t) \cdot 1^{2} + 1^{3} : ln^{3} (t) + 3 ln^{2} (t) + 3 ln (t) + 1

= ln^{3} (t) + 3 ln^{2} (t) + 3 ln (t) + 1

e x p an d \frac{x ^{2} - 7}{( x + 4 ) ( x - 7 )}

e x p an d (x \circ x + 8) (x)

e x p an d (x^{2} sin (x) + 4 y) d y

e x p an d (4, - 1, 0) (8 x - 4 y + z + 9 = 0)

e x p an d \frac{3 Q ( 80000 - Q )}{2000}